The comparison doesn’t work. Maths are abstract, you don’t “believe” in it. You build a consistent theory with minimum assumptions (axioms) and if something stops being consistent, it means some of your assumptions don’t work and you need to change them to build a better theory. Maths is an abstract tool, not a representation of reality.
Infinity is just a concept you can define. There are tools to demonstrate something is true over an infinite space and obviously, you need those for a lot of basic maths. You’re not going to go anywhere in basic arithmetic or geometry if you can’t prove anything works over the infinite set of numbers or the infinite space.
Furthermore, while mathematicians admit that math is entirely man-made construct, which is also the reason we have irrational constant, christian do no such thing.
Imaginary numbers are a perfect example of that. It’s basically just “Okay, in the common number theory, you can’t get the square root of a negative number. What if you could?”. And what do you know, you can build a consistent theory where square root of -1 exists, and it has surprising properties.
Intuitively, good luck trying to make sense of it. But it doesn’t matter, it works, and it’s useful to build other stuff. That in turn can be used as modelling tools in physics and all.
I think it makes sense intuitively. It’s just most of us aren’t really trained since childhood to work with inaginary numbers. Sure, it’s not a 1:1 mapping to your fingers, but it’s not that unintuitive. Like when I do certain calculations I go into a second dimension of numbers where I can move around just as in the first dimension, because those calculations are outside of our current physical reality.
I say current as if our reality will change somehow somewhen lol.
The comparison doesn’t work. Maths are abstract, you don’t “believe” in it. You build a consistent theory with minimum assumptions (axioms) and if something stops being consistent, it means some of your assumptions don’t work and you need to change them to build a better theory. Maths is an abstract tool, not a representation of reality.
Infinity is just a concept you can define. There are tools to demonstrate something is true over an infinite space and obviously, you need those for a lot of basic maths. You’re not going to go anywhere in basic arithmetic or geometry if you can’t prove anything works over the infinite set of numbers or the infinite space.
Furthermore, while mathematicians admit that math is entirely man-made construct, which is also the reason we have irrational constant, christian do no such thing.
Imaginary numbers are a perfect example of that. It’s basically just “Okay, in the common number theory, you can’t get the square root of a negative number. What if you could?”. And what do you know, you can build a consistent theory where square root of -1 exists, and it has surprising properties.
Intuitively, good luck trying to make sense of it. But it doesn’t matter, it works, and it’s useful to build other stuff. That in turn can be used as modelling tools in physics and all.
I think it makes sense intuitively. It’s just most of us aren’t really trained since childhood to work with inaginary numbers. Sure, it’s not a 1:1 mapping to your fingers, but it’s not that unintuitive. Like when I do certain calculations I go into a second dimension of numbers where I can move around just as in the first dimension, because those calculations are outside of our current physical reality.
I say current as if our reality will change somehow somewhen lol.